We present a novel method to compute reduced Teichm\"{u}ller map between shapes. The method operates by iteratively solving Beltrami equation and finally make sure the map's Beltrami coefficient is constant form in each vertex. What is more, we apply Teichm\"{u}ller map to do planar shape interpolation and find that Teichm\"{u}ller map is more efficient than other methods. As we know quasiconformal map is more freedom than conformal map and also quasiconformal map can satisfies our especially request. we can't map a square to a rectangle with matching four corner vertices, but quasiconformal conformal map can realize this. pecially, beltrami coefficient has evidence geometry meaning and we can constructive a smooth, injective and bounded distorted shape interpolation.